I wonder if someone that has not been told to sign or has not been given a deprtation order and then given some sort of leave after 10-11 years even at first the case has been refused, can this be argued as 10 lawful year stay? Thanks

Yes if no removal direction was given and you were on temporary admission and leave is subsequently granted

EXAMPLEA person applies for leave to enter at port on 31 January 1995, and is granted temporaryadmission. The person remains on temporary admission until 27 June 2003, when they aregranted four years leave to enter until June 2007. On 1 February 2005, the person appliesfor indefinite leave under the 10 years rule.Question Has the person completed 10 years continuous lawful residence in the UK?Answer Yes, as the person was granted leave in 2003 following a period of temporaryadmission, their time on temporary admission between 1995 and 2003 countsas lawful residence, and the person has been here lawfully for 10 years.